To make it vegan is simple:
- Replace the milk with any other kind of milk (soy, rice, hemp, etc.)
- Replace butter with some kind of margarine (I recommend Earth Balance, but just pick anything that doesn't have trans fats)
- Replace eggs with either commercial egg replacer, or apple sauce
As for making it moister, I have no idea.
It seems Hamantaschen cookies unfolding and leaking is not an uncommon problem. Of course the flax egg substitution can very likely also contribute to the unfolding but here are some tips from someone who has been baking Hamantaschen cookies for a while.
Tips for Creating Perfect Hamantaschen
1) Find a great dough recipe. Often, the problems people have with
baking hamantaschen can be traced to an inferior dough. Here are two
foolproof, tasty dough recipes that I highly recommend. They are easy
to handle and shape, and they provide great results when baked:
Dairy Free Hamantaschen Dough
Buttery Hamantaschen Dough
Of course you can use your flax egg substituted in for the eggs that the recipes ask for.
2) Roll your dough out to 1/8 inch thick (or less). You want your
dough to be as thin as possible, while still being thick enough to
maintain the cookie’s structure. 1/8 inch seems to be the magic
number; sometimes I roll mine out even thinner than that. For a more
doughy texture you can roll it thicker, but remember– the thicker the
dough is, the harder it will be to handle and shape. Thick dough is
also more prone to opening/spreading in the oven.
3) Use a thick filling that won’t run/weep from the cookies while
baking. Knowing the proper consistency of a hamantaschen filling takes
experience, because each type of filling is slightly different.
Poppyseed filling has a very different texture than fruit filling, for
example. A good filling should be somewhat thick so that it doesn’t
run.
4) Cut your hamantaschen dough in 3-inch circles (or larger) before
filling and folding into triangles. Anything smaller than 3 inches
will be difficult to fold around your chosen filling.
5) Most fillings can be chilled before using to fill hamantaschen.
I’ve found that fruit, poppy seed, and cream cheese-based fillings
tend to be easier to work with when they’re chilled in the
refrigerator. The chilling process thickens the fillings and makes
them less sticky, which makes them easier to handle with when you’re
assembling your hamantaschen. Not all fillings are helped by
refrigeration, however– particularly chocolate-based fillings like
Nutella, which will harden with prolonged refrigeration. Check your
filling recipe to see if refrigeration is recommended.
6) Do not overfill your hamantaschen. Use 1 teaspoon of filling per
hamantaschen cookie. Do not use more than 1 teaspoon. However tempting
it might be to put lots of delicious filling in the middle of your
cookie, using more than 1 teaspoon can cause your hamantaschen to
spread open and leak in the oven. 1 teaspoon is plenty, especially
when you cut your dough circles to 3 inches… it’s the perfect amount
of filling.
7) Fold your triangles the right way! Using the proper folding method
will help your hamantschen hold together and create a beautiful shape.
Please that the sides are folded down so that each "side" has an "end" that is above and an "end" that is below in the fashion of folding the top of a box. This will help in preventing the cookies from unfolding.
Also note in Step 5, to pinch each of the 3 corners gently but firmly.
Source: http://theshiksa.com/2012/03/01/how-to-make-perfect-hamantaschen/
Best Answer
Depending on what you are making, you can easily use just one of the mechanisms to create tiny air bubbles in your finished product. On one end of the spectrum are for example pancakes: you mix just enough to ensure that the baking powder (or soda) is distributed well enough, then bake. On the other side we have sponges that work fine with just a base of beaten eggs and sugar.
A rich pound cake is something like a middle ground: it will actually work even without chemical leaveners, provided the fat and sugar were creamed well, but the baking powder is like an extra “boost”. But you need the creaming step for a simple reason: You need the solid fat to be soft and dispersed enough so that the gas from the baking powder can actually lift the batter and enlarge the existing tiny air bubbles created with creaming. And I find it difficult to think of ways to make a batter without softening the fat, simply because you need to mix the ingredients properly.
And finally: The amount of baking powder that you can add is limited. Use too much and it will negatively affect the cake’s taste.